MC isn't a DVD player like a hardware player. It isn't going to force previews on to you unless you leave previews as forced when you rip. MC plays media files, and if you rip the whole disk, either to whole file system or to ISO, then you can use the DVD menu.
MC doesn't support Blu-ray menus, and therefore will never show you Blu-ray previews. You could rip the previews of course, but they will be separate media files, which you then play directly. Even if you insert a Blu-ray and play it, in my case using DVDfab to decrypt, MC will just play the main movie. In fact it did that for me just yesterday with a new Blu-ray disc.
Regarding Mission Impossible, all of the movies 1 thru 3 show fine and I bought the BluRay collection. I would expect any issue to be apparent with all the movies, not just the 4th one.
The protection mechanisms used by the studios are constantly changing, so it is perfectly normal that the first three of a series of movies may play, but the fourth may not, unless the software you are using removes all forms of protection. As you say your copy of AnyDVD is up to date, then it should rip the movie and make it playable in MC. But only you can confirm that the movie has been ripped correctly. Of course PowerDVD will play it, since it can decrypt the movie anyway, and play directly from the disc if you want.
So, before blaming MC, you need to test if your rips play in other Media Players.
I can't make specific comments about the two disks you have mentioned, Walt Disney Short Films Collection and Mission Impossible IV, as I don't have them. But I do note that there were problems with AnyDVD and MI: IV when it first came out. Maybe there still are problems. You will need to check that out.